We prove the exponential decay in the case n>2, as time goes to
infinity, of regular solutions for the nonlinear beam equation
with memory and weak damping utt+Δ2u−M(‖∇u‖L2(Ωt)2)Δu+∫0tg(t−s)Δu(s)ds+αut=0 in Q^ in a noncylindrical domain of ℝn+1(n≥1) under suitable hypothesis on the scalar
functions M and g, and where α is a positive constant.
We establish existence and uniqueness of regular solutions for any
n≥1.